In order to transmit symbols between a base station and a mobile radio, the symbols are modulated onto a carrier frequency in the transmitter, and are demodulated in the receiver. In this case, the mobile radio must use the same carrier frequency as the base station. However, if there is a discrepancy in the carrier frequency in the mobile radio, the discrepancy must be determined in order subsequently to allow it to be compensated for. A frequency discrepancy such as this in the mobile radio may be caused, for example, by tolerances of the oscillator which produces the carrier frequency. A further cause of frequency shifts may be temperature fluctuations. Furthermore, movements of the mobile radio with respect to the base station lead to Doppler frequency shifts.
As a rule, the phase difference between two successive symbols which are received by the mobile radio is measured in order to determine the discrepancy between the carrier frequency of the mobile radio, in which case it may firstly be necessary to demodulate a known data sequence, which is modulated onto the symbols. Since the received symbols are complex symbols, they can be represented by pointers on the complex number plane. If the two symbols were the same when they generated in the base station, the rotation angle of the associated pointer in the complex numerical plane can be considered for the phase difference between the two received symbols. The phase difference represents a direct measure of the frequency difference between the carrier frequency of the base station and the carrier frequency of the mobile radio.
In the UMTS (Universal Mobile Telecommunications System) Standard, the frequency error of the mobile radio can be determined with the aid of the pilot signal (common pilot channel; CPICH). The pilot signal is a signal which is transmitted by the base station and by means of which the same pilot symbol or a continuously recurring pattern of two different pilot symbols is transmitted continuously. The pilot signal is therefore particularly suitable for the phase difference measurement described above.
The pilot symbols which are received by the mobile radio are referred to in the following text as rk with the integer index k indicating the time sequence of the pilot symbols rk. The frequency discrepancy Δf can be calculated using the following equation (1) from the phase difference Δφ measured between two directly successively received pilot symbols rk-1 and rk:
                              Δ          ⁢                                          ⁢          f                =                  Δφ                      2            ⁢            π            ⁢                                                  ⁢                          T              s                                                          (        1        )            where the time Ts denotes the time interval between the transmission of the pilot symbols rk-1 and rk. The pilot symbol rate is calculated from 1/Ts, and is 15 kHz in the UMTS Standard.
A complex product Uk can be formed from the pilot symbol rk and the complex-conjugate pilot symbol rk-1*:Uk=rk-1*·rk  (2)
The argument of the complex product Uk indicates the phase difference Δφ:
                    Δφ        =                              arg            ⁡                          (                              U                k                            )                                =                      arctan            ⁡                          (                                                Im                  ⁢                                      {                                          U                      k                                        }                                                                    Re                  ⁢                                      {                                          U                      k                                        }                                                              )                                                          (        3        )            
The above equations (1) to (3) provide a calculation rule by means of which the frequency discrepancy Δf of the mobile radio can be estimated. The unambiguity range |Δf| of this estimate is given by:
                                                                    Δ              ⁢                                                          ⁢              f                                            <                      1                          2              ⁢                              T                s                                                    =                  7.5          ⁢                                          ⁢          kHz                                    (        4        )            
For small phase differences Δφ, the variance var(Δ(φ) in the distribution of the phase difference Δφ for additive white Gaussian noise with a signal-to-noise ratio Es/N0 and averaging over L values can be calculated approximately as follows:
                              var          ⁡                      (            Δφ            )                          =                              1                          2              ⁢                              L                2                            ⁢                                                E                  s                                                  N                  0                                                              +                      1                          2              ⁢                                                L                  ⁡                                      (                                                                  E                        s                                                                    N                        0                                                              )                                                  2                                                                        (        5        )            
So far, two pilot symbols rk and rk-1 have been considered, which follow one another directly in the time sequence of the pilot symbols. However, the analysis of two pilot symbols rk and rk-D, which are separated from one another by D symbols in the time sequence of the pilot symbols has certain advantages. In order to make these advantages plausible, the parameter D must be taken into account in the equations (2), (4) and (5):
                              U          k                =                              r                          k              -              D                        *                    ·                      r            k                                              (        6        )                                                                                Δ              ⁢                                                          ⁢              f                                            <                      1                          2              ⁢                              T                s                            ⁢              D                                      =                              7.5            ⁢                                                  ⁢            kHz                    D                                    (        7        )                                          var          ⁡                      (            Δφ            )                          =                              1                          2              ⁢                              DL                2                            ⁢                                                E                  s                                                  N                  0                                                              +                      1                          2              ⁢                              D                2                            ⁢                                                L                  ⁡                                      (                                                                  E                        s                                                                    N                        0                                                              )                                                  2                                                                        (        8        )            
The advantage of the introduction of the parameter D can be seen from equation (8): an increase in the parameter D leads to a reduction in the variance var(Δφ). However, an increase in the parameter D in equation (7) also leads to a reduction in the unambiguity range |Δf|.
When the base station is being operated in the STTD (Space Time Transmit Diversity) mode, the radio signal is transmitted from two base station antennas. In this case, the complex product Uk must be calculated separately for the two antennas.
In the case of known mobile radios, the discrepancy between the carrier frequency of the mobile radio and the carrier frequency of the base station is calculated completely in the firmware by means of a digital signal processor. If a number of base stations and a number of transmission paths for each base station are investigated in this case, then all of the data is transmitted on a path-specific basis to the digital signal processor. This leads to a high work load on both the digital signal processor and the data bus via which the data is transmitted.